BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Solutions

Chapter
Section
BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

Naturally occurring 40K is listed as responsible for 16 mrem/y of background radiation. Calculate the mass of 40K that must be inside the 55−kg body of a woman to produce this dose. Each 40K decay emits a 1.32−MeV β, and 50% of the energy is absorbed inside the body.

To determine

The mass of 40K that must be inside a 55 kg body of a woman to produce a dose of 16 mrem/y of background radiation if 50% of the energy is absorbed by the body.

Explanation

Given info:

The background radiation dose

  dose=16 mrem/y

Mass of the woman's body

  m=55 kg

Energy of the emitted β particle

  Eβ=1.32MeV

Half-life of 40K

  t1/2=1.251×109y

Formula used:

The activity of a radioactive sample is given by,

  R=0.693Nt1/2

Here, N is the number of atoms of the radioactive substance present.

The dose in rem is related to the dose in rad as follows:

  dose in rem= dose in rad×RBE

Here RBE is the relative biological effectiveness.

Calculation:

Express the radiation dose in rad.

  dose in rad=dose in remRBE

The RBE for β particle is 1.

Therefore,

  dose in rad=dose in remRBE=16 mrem/y1=16 mrad/y

Express the dose per year in J/kg.

  dose in rad=16 mrad/y× 10 3rad1 mrad×0.01 J/kg1 rad=1.60×104J/kgy

The energy deposited in the woman for the radiation of the energy for a year as calculated above is given by,

  E=radiation dose×mass of the woman

Therefore,

  E=radiation dose×mass of the woman=1.60× 10 4J/kgy55 kg=8.80×103J/y

Express the energy in MeV/y.

  E=8.80×103J/y×1 MeV1.6× 10 13J=5

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

Osteoporosis occurs during the late years of life; however, it is a disease that develops while one is young. C...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

Why is degenerate matter so difficult to compress?

Horizons: Exploring the Universe (MindTap Course List)

What is the chief chemical property of ethers?

Chemistry for Today: General, Organic, and Biochemistry

When a high-power laser is used in the Earths atmosphere, the electric field associated with the laser beam can...

Physics for Scientists and Engineers, Technology Update (No access codes included)